I now play Hauptwerk through a Roland Atelier at90s organ. This works fine except that I get computer noise from my Mac Mini carried over to the Roland organ speakers which can be quite noticeable at times. Is anything I can do the eliminate this from happening or minimize it?
The only noise a computer makes are from cooling fans, either from the PSU (power supply), the CPU (processor), or a GPU (graphics card). Audio noise can originate from a program via the audio card. Can't recall any other noise as originating from the computer itself.
First thing to do is just reposition the computer and its associated wires and see if that helps. A few feet can make all the difference. Many times, that is all it takes. Adding RF chokes to the wires going to and from the computer would be the next thing to try.
After trying Ed's suggestion, see if you can get/borrow a different power supply for the mini. A blown/going capacitor can cause these problems, if they weren't there before.